Because cooking souffls is incredibly difficult, the supply of souffls in a small French town is controlled

Because cooking soufflés is incredibly difficult, the supply of soufflés in a small French town is controlled by two bakers, Gaston and Pierre. The demand for soufflés is given by P = 30 - 2Q, and the marginal and average total cost of producing soufflés is $6. Because baking a soufflé requires a great deal of work and preparation, each morning Gaston and Pierre make a binding decision about how many soufflés to bake.
a. Suppose that Pierre and Gaston agree to collude, evenly splitting the output a monopolist would make and charging the monopoly price.
i. Derive the equation for the monopolist's marginal revenue curve.
ii. Determine the profit-maximizing collective output for the cartel.
iii. Determine the price Pierre and Gaston will be able to charge.
iv. Determine profits for Pierre and Gaston individually, as well as for the cartel as a whole.
b. Suppose that Pierre cheats on the cartel agreement by baking one extra soufflé each morning.
i. What does the extra production do to the price of soufflés in the marketplace? ii. Calculate Pierre's profit. How much did he gain by cheating? iii. Calculate Gaston's profit. How much did Pierre's cheating cost him? iv. How much potential profit does the group lose as a result of Pierre's cheating?
c. Suppose that Gaston, fed up with Pierre's behavior, also begins baking one extra soufflé each morning.
i. How does the extra production affect the price of soufflés in the marketplace? ii. Calculate Gaston's profit. How much did he gain by cheating? iii. Calculate Pierre's profit. How much did Gaston's cheating cost him? iv. How much potential profit does the group lose as a result of Pierre's and Gaston's cheating?
v. Demonstrate that it is in neither Pierre's nor Gaston's best interest to cheat further on their agreement.